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Deconstructing Lawvere with distributive laws

Bonchi, F; Sobocinski, P; Zanasi, F; (2018) Deconstructing Lawvere with distributive laws. Journal of Logical and Algebraic Methods in Programming , 95 pp. 128-146. 10.1016/j.jlamp.2017.12.002. Green open access

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Abstract

PROs, PROPs and Lawvere categories are related notions adapted to the study of algebraic structures borne by an object in a category: PROs are monoidal, PROPs are symmetric monoidal and Lawvere categories are cartesian. This paper connects the three notions using Lack's technique for composing PRO(P)s via distributive laws. We show that Lawvere categories can be seen as the composite PROP , where expresses the algebraic structure in linear form and express the ability of copying and discarding them. In turn the PROP can be decomposed in terms of PROs as where expresses the ability of permuting variables and is the PRO encoding the syntactic structure without permutations.

Type: Article
Title: Deconstructing Lawvere with distributive laws
Open access status: An open access version is available from UCL Discovery
DOI: 10.1016/j.jlamp.2017.12.002
Publisher version: http://doi.org/10.1016/j.jlamp.2017.12.002
Language: English
Additional information: © 2017 Elsevier Inc. All rights reserved. This version is the author accepted manuscript. For information on re-use, please refer to the publisher’s terms and conditions.
Keywords: Science & Technology, Technology, Computer Science, Theory & Methods, Logic, Computer Science, Science & Technology - Other Topics, MONOIDAL CATEGORIES, ALGEBRA, MONADS, GRAPHS
UCL classification: UCL
UCL > Provost and Vice Provost Offices
UCL > Provost and Vice Provost Offices > UCL BEAMS
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Engineering Science
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Engineering Science > Dept of Computer Science
URI: https://discovery.ucl.ac.uk/id/eprint/10046407
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